KKostya

Keybase proof

I hereby claim:

• I am kkostya on github.
• I am kostya_imandra (https://keybase.io/kostya_imandra) on keybase.
• I have a public key ASCUVV8FQdvjmwaYjg9M7DChJknkKWODHPKVNRGu1OrsgAo

To claim this, I am signing this object:

KKostya

#include <functional>
class A {};
class B {};

typedef std::function<B(A)> F;
typedef std::function<B(F)> G;
typedef std::function<B(G)> H;

F proof(H h){
  auto t = [](A a){

KKostya

pairwise = lambda b: zip(*((lambda a: (lambda x: (next(x[1]), x))((iter(a), iter(a))))(b)[1]))

KKostya

# Python3 implementation of Heap's algorithm
# https://en.wikipedia.org/wiki/Heap%27s_algorithm
def heap(lst, k=None):
    if k is None: k = len(lst)
    if k == 1: 
        yield(tuple(lst))
        return
    yield from heap(lst, k - 1)
    for i in range(k-1):
        m = i if k % 2 == 0 else 0

KKostya

instance ( (strategy) => Real.({
  valid_strategy(strategy) &&
  ( expected_reward (
      make_scenario_pmf(pDoorsEqual,strategy)
  ) == 2000000.0 / 3.0 ) 
}))

KKostya

verify ( (strategy) => Real.({
  valid_strategy(strategy) ==>
  ( expected_reward (
      make_scenario_pmf(pDoorsEqual,strategy)
  ) <= 2000000.0 / 3.0 ) 
}))

KKostya

let pDoorsEqual : (door => real) = (door) => Real.(1.0 / 3.0)

KKostya

let random_then_swap_strategy = (door : door,choice) => 
    switch(door,choice){ | (_,Swap) => Real.(1.0 / 3.0) | _ => 0.0 };
expected_reward(
  make_scenario_pmf(pDoorsEqual,random_then_swap_strategy)
)

KKostya

verify ( (strategy) => Real.({
  valid_strategy(strategy) ==>
  ( expected_reward (
      make_scenario_pmf(pDoorsBiased,strategy)
  ) <= 800000.0 ) 
}))

KKostya

let aStayStrategy = (door,choice) => 
    switch(door,choice){ | (DoorA,Stay) => 1.0 | _ => 0.0 };
expected_reward(
  make_scenario_pmf(pDoorsBiased,aStayStrategy)
);
let cSwapStrategy = (door,choice) => 
    switch(door,choice){ | (DoorC,Swap) => 1.0 | _ => 0.0 };
expected_reward(
  make_scenario_pmf(pDoorsBiased,cSwapStrategy)
);